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Learn/ A Level Mathematics/ Past Papers/ 2023/ Oct/Nov 2023 /Paper 2 (Variant 3)

Pure Mathematics 2 — Variant 3

A Level Mathematics · 9709/23 · Oct/Nov 2023

Question Paper

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Mark Scheme

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Questions

3 of 7 questions shown here, checked against the paper. The others are in the PDF above — they contain diagrams or maths we could not yet verify, and we would rather show you the original than a transcription we are not sure of.

3
3(a) [4]
Find ∫41042x−5 dx\int_{4}^{10} \frac{4}{2x - 5} \, \mathrm{d}x, giving your answer in the form ln⁡a\ln a, where aa is an integer.
3(b) [2]
Find the exact value of ∫410e2x−5 dx\int_{4}^{10} \mathrm{e}^{2x-5} \, \mathrm{d}x.
4
4(a) [2]
Sketch, on the same diagram, the graphs of y=∣3x−5∣y = |3x - 5| and y=2x+7y = 2x + 7.
4(b) [3]
Solve the equation ∣3x−5∣=2x+7|3x - 5| = 2x + 7.
4(c) [2]
Hence solve the equation ∣3y+1−5∣=2×3y+7|3^{y+1} - 5| = 2 \times 3^{y} + 7, giving your answer correct to 3 significant figures.
7
The curve with equation e2x−18x+y3+y=11\mathrm{e}^{2x} - 18x + y^{3} + y = 11 has a stationary point at (p,q)(p, q).
7(a) [4]
Find the exact value of pp.
7(b) [2]
Show that q=2+18ln⁡3−q3q = \sqrt[3]{2 + 18\ln 3 - q}.
7(c) [2]
Show by calculation that the value of qq lies between 2.5 and 3.0.
7(d) [3]
Use an iterative formula, based on the equation in (b), to find the value of qq correct to 4 significant figures. Give the result of each iteration to 6 significant figures.

Published by Cambridge Assessment International Education. Reproduced for study use.